Class 11

Math

JEE Main Questions

Binomial Theorem

If and b are distinct integers, prove that $a−b$is a factor of $a_{n}−b_{n}$, whenever n is a positive integer.

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Find $a$ if the 7th and 18th terms of the expansion $(2+a)_{50}$ are equal.

Find the greatest term in the expansion of $3 (1+3 1 )_{20}˙$

In the coefficients of rth, $(r+1)th,and(r+2)th$ terms in the binomial expansion of $(1+y)_{m}$ are in A.P., then prove that $m_{2}−m(4r+1)+4r_{2}−2=0.$

Find the remainder when $5_{99}$ is divided by 13.

If $10_{m}$ divides the number $101_{100}−1$ then, find the greatest value of $m˙$

Find the last three digits of the number $27_{27}˙$

Show that $9_{n+1}−8n−9$ is divisible by 64, where $n$ is a positive integer.

If $9_{7}+7_{9}$ is divisible b $2_{n},$ then find the greatest value of $n,wheren∈N˙$